11H71 26A46 93B17 tail set 11B39 11B83 60G50 Hausdorff-Besicovitch dimension Jacobsthal-Lucas sequence \(G_2\)-representation of numbers \(\Delta^{\mu}\)-representation continuous transformation of \((0,1]\) preserving ``tails'' of \(\Delta^{\mu}\)-representation of numbers cylinder cylindrical set (cylinder) function preserving ``tails'' of \(\Delta^{\mu}\)-representation of numbers group of continuous transformations of real interval preserving tails left and right shift operator set of incomplete sums singular random variable two-symbol system of encoding (representation) of numbers